Analysis and design of discrete-time networked systems over fading channels

This paper considers the feedback stabilization and performance design of an SISO plant controlled over a single channel. The channel undergoes both fading and additive noise, and its input power is bounded by a predefined level. We show that there exists a minimal requirement on the network over which an unstable plant can be stabilized via dynamic output feedback. The requirement relates the statistics of channel fading and channel additive noise as well as the power bound of channel input with the Mahler measure of the plant. It is demonstrated that the scaling factor of the network plays an essential role in satisfying the power constraint. A suboptimal algorithm is proposed for performance design of the networked control system. At last, a numerical example is provided to illustrate the validity of the results.